Relax-and-round strategies for solving the Unit Commitment problem with AC Power Flow constraints

TL;DR

The paper tackles the Unit Commitment problem with AC power flow constraints ($UC{-}ACOPF$), a non-convex MINLP, by studying relax-and-round heuristics that start from the continuous relaxation and aim to recover integer feasibility. It introduces a model-based rescaling of the relaxed commitment variables and specialized rounding formulas to preserve combinatorial structure and AC feasibility, comparing them against standard direct rounding on 6-bus and 118-bus test systems. The approaches are embedded into a PSLP solver framework and further integrated into a Feasibility Pump (FP) to broaden applicability. Results show improved UC and AC feasibility rates and faster convergence in many cases, indicating these heuristics as practical, fast alternatives for obtaining AC-feasible points in time-sensitive settings. The methods have potential for real-time or near-real-time operation where rapid feasibility is crucial, and they offer a flexible blueprint for combining relax-and-round ideas with FP in complex power-system optimization.

Abstract

The Unit Commitment problem with AC power flow constraints (UC-ACOPF) is a non-convex mixed-integer nonlinear programming (MINLP) problem encountered in power systems. Its combination of combinatorial complexity and non-convex nonlinear constraints makes it particularly challenging. A common approach to tackle this issue is to relax the integrality condition, but this often results in infeasible solutions. Consequently, rounding heuristics are frequently employed to restore integer feasibility. This paper addresses recent advancements in heuristics aimed at quickly obtaining feasible solutions for the UC-ACOPF problem, focusing specifically on direct relax-and-round strategies. We propose a model-based heuristic that rescales the solution of the integer-relaxed problem before rounding. Furthermore, we introduce rounding formulas designed to enforce combinatorial constraints and aim to maintain AC feasibility in the resulting solutions. These methodologies are compared against standard direct rounding techniques in the literature, applied to a 6-bus and a 118-bus test systems. Additionally, we integrate the proposed heuristics into an implementation of the Feasibility Pump (FP) method, demonstrating their utility and potential to enhance existing rounding strategies.

Figures (7)

• Figure 2: 6-bus test system circuit.
• Figure 3: Active power generation in the 6-bus test system example.
• Figure 4: Reactive power generation in the 6-bus test system example.
• Figure : (a) Generation unit 1.
• Figure : (a) Generation unit 1.